A community for students.
Here's the question you clicked on:
 0 viewing
sritama
 4 years ago
a1,a2,a3....a30each of these 30 sets has 5 elements.b1,b2,....bneach of these n sets has 3 elements.union of a1,a2...a30=union of b1,b2....bn=S.
if each elements of S is in 10 a sets and 9 bsets.then n=?
ans=45.
show the process
sritama
 4 years ago
a1,a2,a3....a30each of these 30 sets has 5 elements.b1,b2,....bneach of these n sets has 3 elements.union of a1,a2...a30=union of b1,b2....bn=S. if each elements of S is in 10 a sets and 9 bsets.then n=? ans=45. show the process

This Question is Closed

joemath314159
 4 years ago
Best ResponseYou've already chosen the best response.1ok, here we go~ So the number of elements in the union of the A sets is: \[5(30)r_A\]where r is the number of repeats. Likewise the number of elements in the B sets is: \[3nr_B\] Each element in the union (in S) is repeated 10 times in A, which means if x was the real number of elements in A (not counting repeats) then 9 out of those 10 should be thrown away, or 9x. Likewise on the B side, 8x of those elements should be thrown away. so now we have: \[1509x = 3n8x \iff 150x = 3n \iff 50\frac{x}{3} = n\] Now, to figure out what x is, we need to use the fact that the union of a group of sets contains every member of each set. if every element in S is repeated 10 times, that means every element in the union of the A's is repeated 10 times. This means that: \[\frac{150}{10} = 15\]is the number of elements in the the A's without repeats counted (same for the Bs as well). So now we have: \[50\frac{15}{3} = n \iff n = 45\]

sritama
 4 years ago
Best ResponseYou've already chosen the best response.0i understand.r u a teacher?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.